Calculate Rectangle Perimeter: Area = 32 Square Units (8 × 4)

Q: Why do I multiply by 2 in the perimeter formula?

A rectangle has four sides, but opposite sides are equal! So you have two sides of length 8 and two sides of length 4. That's why we use $ P = 2(8 + 4) $ instead of adding all four sides separately.

Q: What if I only know the area but not the individual sides?

You'd need additional information! With just Area = 32, there are many possible rectangles (like 1×32, 2×16, 4×8). This problem gives you the diagram showing the specific dimensions.

Q: Can I just add all four sides instead of using the formula?

Absolutely! You can calculate $ 8 + 4 + 8 + 4 = 24 $. The formula $ P = 2(l + w) $ is just a shortcut that does the same thing more efficiently.

Q: How can I double-check my perimeter answer?

Verify that the given area matches your dimensions: $ 8 \times 4 = 32 $ ✓. Also check that your perimeter uses all four sides of the rectangle.

Rectangle Perimeter with Given Area

The area of a rectangle is equal to 32.

Calculate the perimeter of the rectangle.

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Understand the problem

The area of a rectangle is equal to 32.

Calculate the perimeter of the rectangle.

Step-by-step solution

Since we know that each pair of opposite sides in a rectangle are equal, we also know that:

$AC=BD=4$

$AB=CD=8$

Now we can calculate the perimeter:

$4\times2=8$

$8\times2=16$

$16+8=24$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals sum of all four sides
Technique: Use P = 2(length + width) = 2(8 + 4)
Check: Verify area: length × width = 8 × 4 = 32 ✓

Common Mistakes

Avoid these frequent errors

Confusing area and perimeter formulas
Don't use Area = 32 as the perimeter! Area measures space inside (length × width), while perimeter measures distance around the outside. Always use P = 2(length + width) for rectangle perimeter.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

Why do I multiply by 2 in the perimeter formula?

A rectangle has four sides, but opposite sides are equal! So you have two sides of length 8 and two sides of length 4. That's why we use $P = 2(8 + 4)$ instead of adding all four sides separately.

How do I know which measurement is length and which is width?

It doesn't matter! In this problem, you can call 8 the length and 4 the width, or vice versa. The perimeter will be the same either way: $2(8 + 4) = 2(4 + 8) = 24$ .

What if I only know the area but not the individual sides?

You'd need additional information! With just Area = 32, there are many possible rectangles (like 1×32, 2×16, 4×8). This problem gives you the diagram showing the specific dimensions.

Can I just add all four sides instead of using the formula?

Absolutely! You can calculate $8 + 4 + 8 + 4 = 24$ . The formula $P = 2(l + w)$ is just a shortcut that does the same thing more efficiently.

How can I double-check my perimeter answer?

Verify that the given area matches your dimensions: $8 \times 4 = 32$ ✓. Also check that your perimeter uses all four sides of the rectangle.

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